Question

one of the most efficient engines ever develop operates bet 2100k & 700k.It's actual efficiency is 40% .What percentage of it's Max possible efficiency . Explain it step by step...​

Answer 1

$\bigstar$ Answer

Maximum efficiency = 60 %

$\bigstar$ Explanation

$\checkmark$ Given:

One of the most efficient engines ever develop operates bet 2100 K & 700 K. It's actual efficiency is 40 %

$\checkmark$ To Find:

What percentage of it's Maximum possible efficiency

$\checkmark$ Solution:

We know that,

Efficiency of Engine ( η )

$\green{\implies \sf \eta=1-\dfrac{T_{c}}{T_{h}}}$

Here,

• $\eta$ = Efficiency
• $\sf T_{c}$ = Temp. at cool region
• $\sf T_{h}$ = Temp. at hot region

Given that,

One of the most efficient engines ever develop operates bet 2100 K & 700 K. It's actual efficiency is 40 %

Hence,

• $\sf T_{c}$ = 700 K
• $\sf T_{h}$ = 2100 K

Therefore,

By Substituting the values,

We get,

$\implies \sf \eta=1-\dfrac{700}{2100}$

$\implies \sf \eta=\dfrac{2}{3}$

Also Given that,

It's actual efficiency is 40 %

Hence,

Actual Efficiency = 0.4

According to the Question,

We are asked to find the percentage of it's Maximum possible efficiency

Hence,

Maximum possible efficiency ( $\eta'$ )

$\blue{\sf \implies \eta'=\dfrac{0.4}{\dfrac{2}{3}} \times 100}$

$\sf \implies \eta'=\dfrac{6}{10} \times 100$

$\red{\sf \implies \eta'=60\%}$

Hence,

$\checkmark$ Maximum efficiency = 60 %